Buddies Dive at Bonaire comes to mind. With rented trucks and unlimited shore diving, it lets you set your own schedule for the day. You imply many/several divers so then several schedules can be met.
Another idea is Osprey Beach hotel on Grand Turk. We loved it but its harder to get to. Its a VERY quiet island with diving about 3-6 min from the beach. We used Oasis diving. They do their surface intervals at shore so you can single/double/triple dive whenever the need/desire hits.
Ocean Frontiers on Grand Cayman has the BEST dive service I have ever had over my 20+ yrs of diving. They can arrange a place to stay but I have not tried their offerings for a hotel. You setup your gear once and never touch it again. they break it down, rinse it, hang it, you tell them when you are back and they have it setup in the boat for you. Luxurious!
You want a real BUDGET outing, then try the SeaGrape on Roatan. check their website for pricing but you can have 7 nights and 12 dives for about $600 per person if you share rooms. Having your own room is not expensive either. diving is west end of Roatan which is nice but perhaps not spectacular. We had a really good time. They let me add 3rd dives per day for a really low price. If I was the only diver, they went anyway! The dive guide wanted to dive too.
So there are a few ideas. Hope that helps a bit.
